The Republic of Ireland stopper spent 12 years at St. James Park before becoming Mark Hughes' fourth big money signing during the winter transfer window.
And the glove-man believes that - after a dozen years' loyal service to the Magpies - he deserved better treatment from his former club.
"I felt Newcastle could have dealt with it a little bit better," he said at a press conference unveiling him as the Blues's new No.37.
"It's nearly 12 years of my life so it's a long time and I would to thank the fans for the support they've given me over those years. They've been absolutely phenomenal. Now it's time for a new challenge, a new set of supporters to impress.
"I just felt after the service I'd given the club, the regime could have looked after the thing a whole lot better."
"They made me do things I didn't want to do in the end. I felt this was a great opportunity for me to further my career and go on and pick up some silverware and I'm disappointed with the way the regime handled things.
Given conceded Newcastle's perilous plight was a contributing factor to his desire to seek fresh challenges elsewhere, with the Magpies's poor performances and results steadily chipping away at morale.
" I just felt the last six months it's been fizzling out," he said. "It's not been enjoyable going into training and stuff. From a selfish point of view, I deserved a bit better than that and I wanted to be challenging for honours. I didn't want to be regretting at the end of my career not taking this opportunity.
"The Liverpool game at home [a 5-1 thrashing on December 28] was such a lowpoint in my career. I just felt walking off the pitch, that if I never saw a football again, I'd be happy, I was that low. A lot people were saying I was happy at the club but I wasn't comfortable at the club."
Given's quest for silverware on Tyneside ultimately proved unsuccessful during his 12-year stint - coming close to lifting the FA Cup in both 1998 and 1999, losing in the final to Arsenal and Manchester United respectively.
And he feels that, at City, he now has a chance of tasting some success that his consistent performances over the years have deserved.
"I went to Newcastle to try and win something and that didn't materialise. I think I'm joining a club now who have a real opportunity of picking up silverware.
"I'm 32, in goalkeeping terms it's still relatively young, and I'd like to think I can play for a good number of years yet."
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